Let $f(x) = \cos(\sqrt{P}x),$ where $P = [\lambda]$ and $[.]$ denotes the Greatest Integer Function. If the period of $f(x)$ is $\pi$,then:

If set $A$ has $5$ elements and set $B$ has $7$ elements,then the number of many-one functions that can be defined from $A$ to $B$ is:

For the greatest integer function $f(x) = [x]$,where $x \in R$,which of the following is true?

Let $f: X \rightarrow X$ be such that $f(f(x)) = x$ for all $x \in X$ and $X \subseteq \mathbb{R}$. Then:

Let $A = \{1, 2, 3, 4\}$ and $R : A \to A$ be the relation defined by $R = \{ (1, 1), (2, 3), (3, 4), (4, 2) \}$. The correct statement is

If $f(x) = \begin{cases} x, & \text{when } x \text{ is rational} \\ 0, & \text{when } x \text{ is irrational} \end{cases}$ and $g(x) = \begin{cases} 0, & \text{when } x \text{ is rational} \\ x, & \text{when } x \text{ is irrational} \end{cases}$,then $(f - g)$ is: